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Large deviation principles for stationary processes. (English) Zbl 0659.60051

The authors establish a level-three type large deviation theorem for stationary sequences with values in a compact separable metric space under a ratio-mixing condition for associated conditional probabilities. Under an additional continuity assumption they identify the rate function as a relative entropy. The authors relate their results to those of Donsker and Varadhan and apply the main theorems to a certain class of Gibbs measures.
Reviewer: M.Scheutzow

MSC:

60F10 Large deviations
60G10 Stationary stochastic processes
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